When you simplify $\sqrt[3]{24a^4b^6c^{11}}$, what is the sum of the exponents of the variables that are outside the radical?
Factor the radicand, to yield $\sqrt[3]{24a^4b^6c^{11}} = \sqrt[3]{(2^3a^3b^6c^9)3ac^2} = 2ab^2c^3\sqrt[3]{3ac^2}$.  The sum of the exponents of $a$, $b$, and $c$ outside the radical is $1+2+3=\boxed{6}$.